code: def _single_variance_gradient(tape, var_mask, pdA2, f0, pdA):
      """Auxiliary function to return the derivative of variances.
  
      return d(var(A))/dp = d<A^2>/dp -2 * <A> * d<A>/dp for the variances (var_mask==True)
      d<A>/dp for plain expectations (var_mask==False)
  
      Note: if isinstance(pdA2, int) and pdA2 != 0, then len(pdA2) == len(pdA)
  
      """
      num_params = len(tape.trainable_params)
      num_measurements = len(tape.measurements)
      if num_measurements > 1:
          if num_params == 1:
              var_grad = []
  
              for m_idx in range(num_measurements):
                  m_res = pdA[m_idx]
                  if var_mask[m_idx]:
                      pdA2_comp = pdA2[m_idx] if pdA2 != 0 else pdA2
                      f0_comp = f0[m_idx]
                      m_res = _get_var_with_second_order(
                          pdA2_comp, f0_comp, m_res
                      )
  
                  var_grad.append(m_res)
              return tuple(var_grad)
  
          var_grad = []
          for m_idx in range(num_measurements):
              m_res = []
              if var_mask[m_idx]:
                  for p_idx in range(num_params):
                      pdA2_comp = (
                          pdA2[m_idx][p_idx] if pdA2 != 0 else pdA2
                      )
                      f0_comp = f0[m_idx]
                      pdA_comp = pdA[m_idx][p_idx]
                      r = _get_var_with_second_order(
                          pdA2_comp, f0_comp, pdA_comp
                      )
                      m_res.append(r)
                  m_res = tuple(m_res)
              else:
                  m_res = tuple(
                      pdA[m_idx][p_idx] for p_idx in range(num_params)
                  )
              var_grad.append(m_res)
          return tuple(var_grad)
  
      # Single measurement case, meas has to be variance
      if num_params == 1:
          return _get_var_with_second_order(pdA2, f0, pdA)
  
      var_grad = []
  
      for p_idx in range(num_params):
          pdA2_comp = pdA2[p_idx] if pdA2 != 0 else pdA2
          r = _get_var_with_second_order(pdA2_comp, f0, pdA[p_idx])
          var_grad.append(r)
  
      return tuple(var_grad)
  
imports: from typing import Sequence, Callable
  from functools import partial
  import numpy
  import pennylane
  from pennylane.measurements import VarianceMP
  from pennylane import transform
  from pennylane.transforms.tape_expand import expand_invalid_trainable
  from pennylane.gradients.gradient_transform import _contract_qjac_with_cjac
  from .finite_difference import finite_diff
  from .general_shift_rules import _iterate_shift_rule, frequencies_to_period, generate_shifted_tapes, process_shifts
  from .gradient_transform import _all_zero_grad, assert_no_state_returns, assert_no_tape_batching, assert_multimeasure_not_broadcasted, choose_trainable_params, find_and_validate_gradient_methods, _no_trainable_grad, reorder_grads
label_desc: Use image node_id 14 for calling a global function with example usage: _single_variance_gradient(tape, var_mask, pdA2, f0, pdA) and returns: tuple, tuple, _get_var_with_second_order, tuple